A Geometric Interpretation of the Intertwining Number
Combinatorics
2018-07-09 v1
Abstract
We exhibit a connection between two statistics on set partitions, the intertwining number and the depth-index. In particular, results link the intertwining number to the algebraic geometry of Borel orbits. Furthermore, by studying the generating polynomials of our statistics, we determine the specialization of a -analogue of the Bell numbers. Finally, by using Renner's -polynomial of an algebraic monoid, we introduce and study a -analog of -Stirling numbers.
Cite
@article{arxiv.1807.02156,
title = {A Geometric Interpretation of the Intertwining Number},
author = {Mahir Bilen Can and Yonah Cherniavsky and Martin Rubey},
journal= {arXiv preprint arXiv:1807.02156},
year = {2018}
}
Comments
15 pages